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Complex numbers are an intrinsic part of the mathematical formalism of quantum theory and are perhaps its most characteristic feature. In this article, we show that the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability… (More)

- Philip Goyal, Kevin H. Knuth
- Symmetry
- 2011

Quantum theory is a probabilistic calculus that enables the calculation of the probabilities of the possible outcomes of a measurement performed on a physical system. But what is the relationship between this probabilistic calculus and probability theory itself? Is quantum theory compatible with probability theory? If so, does it extend or generalize… (More)

- Philip Goyal
- Information
- 2012

The concept of information plays a fundamental role in our everyday experience, but is conspicuously absent in framework of classical physics. Over the last century, quantum theory and a series of other developments in physics and related subjects have brought the concept of information and the interface between an agent and the physical world into… (More)

Physics is real. Measurement produces real numbers. Yet quantum mechanics uses complex arithmetic, in which √ −1 is necessary but mysteriously relates to nothing else. By applying the same sort of symmetry arguments that Cox [1, 2] used to justify probability calculus, we are now able to explain this puzzle. The dual device/object nature of observation… (More)

- Philip Goyal
- 2005

Abstract. General theoretical principles that enable the derivation of prior probabilities are of interest both in practical data analysis and, more broadly, in the foundations of probability theory. In this paper, it is shown that the general rule for the assignment of priors proposed by Jeffreys can be obtained from, and is logically equivalent to, an… (More)

- Philip Goyal
- 2012

The framework of classical physics is based on a mechanical conception of nature, a conception which is mirrored in the Turing model of computation. Quantum theory has, however, fundamentally challenged this conception. The mathematical formalism of quantum theory consists of a set of postulates, most of which are at odds with the corresponding postulates… (More)

- Philip Goyal
- 2011

Quantum theory poses deep challenges to the mechanical conception of reality that underlies classical physics. Yet today, over eighty years after its creation, its implications for our picture of reality remain enshrouded in uncertainty. In view of the current search for a more comprehensive theory of physics (a so-called theory of everything), it is vital… (More)

- Klil H. Neori, Philip Goyal
- 2014

The operational formalism to quantum mechanics seeks to base the theory on a firm foundation of physically well-motivated axioms [1]. It has succeeded in deriving the Feynman rules [2] for general quantum systems. Additional elaborations have applied the same logic to the question of identical particles, confirming the so-called Symmetrization Postulate… (More)

- ORGANISING COMMITTEE, Philip Goyal, +5 authors Adom Giffin
- 2011

BAYESIAN DATA ANALYSIS: A GENTLE INTRODUCTION G. Tenti Department of Applied Mathematics University of Waterloo Abstract The analysis of experimental data is essential to the development of scientific theories, but the type of reasoning used in formulating hypotheses and having them substantiated by the data has been the subject of great controversies for… (More)

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